1)
We know that normal form of learning curve is given by
Yx=Kxn
Where
K=Direct labor hours needed for first unit=10 hours
x=unit number=4
Yx= labor hours needed for xth unit i.e. 4th unit=8.1 hours
n=log10b/log102 and b=learning percentage
We can estimate the value of n with the help of given equation
Yx=Kxn
8.1=10*4n
0.81=4n
Taking natural log both sides
ln(0.81)=nln(4)
n=ln(0.81)/ln(4)=-0.152
Now we can find the value of b
n=log10b/log102
-0.152=log10b/0.301030
log10b=-0.152*0.301030=-0.04576
b=10-0.04576=0.90
So, Learning percentage=90%
b)
Let us find the time required for 500th unit
Yx=Kxn
Y500=10*(500)-0.152=3.888 minute
Labor Cost=3.888*10=$38.88
Overhead =10% of labor cost=38.88*10%=$3.89
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